Liu & Mahadevan method

The criterion of Liu & Mahadevan [LM05], [Liu06] belongs to the section of methods defining critical plane deviation. The method is based on a distinction of two different important planes. The first one is the fatigue fracture plane, which is the plane on which the final crack governed by the maximum principal stress is detected. The other plane is the characteristic plane, which needn’t coincide with the fatigue fracture plane.

The criterion obeys a law on the characteristic plane:

There are two material parameters, the third is the angle between fatigue fracture and characteristic planes. The way, how these values are related, is:



k = 0

The table above distinguishes two different modes of fatigue initiation, which is related to the fatigue limit ratio. The breakpoint is set to the value 1. Thus, the very brittle materials are separated from other brittle materials, hard steels or mild steels. The very brittle materials have the both defined planes (the fatigue fracture and characteristic plane) coincident. The influence of hydrostatic stress on the fatigue performance of any other material is erased with the parameters described above. More on their derivation can be found e.g. in [Liu06], which is freely accessible on the Internet. A large comparison of the predictive efficiency of the method can be seen in the [FatLim Database].

Nomenclature:

Mark	Unit	PragTic variable	Meaning
	[MPa]		shear stress amplitude on an examined plane
	[MPa]	TENS-1, BEND-1	fatigue limit in fully reversed axial loading
	[MPa]		amplitude of hydrostatic stress
	[-]		ratio of fatigue limits ()
	[MPa]		amplitude of normal stress on the plane examined
	[MPa]		mean (average value of maximum and minimum values) normal stress on the plane examined
	[MPa]	TORS-1	fatigue limit in fully reversed torsion

Methods & Options & Variables of Calculation – Edit

Decomposition

- Whole load path

Elasto-plasticity

- No – currently no option implemented

Solution option

- Number of scanned planes

- Only every x-th data-point taken from load history

- Evaluate envelope curve only <1~yes, 0~no>

Solution variable

- Minimum damage – this option is not active for this high-cycle fatigue method

Material parameters

E	[MPa]	tensile modulus
NU	[-]	Poisson’s ratio
TENS-1	[MPa]	fatigue limit in fully reversed push-pull (or plane bending)
TORS-1	[MPa]	fatigue limit in fully reversed torsion

Result detail variables

Damage fatigue index is computed, not the damage as a reciprocal value to number of cycles or repetitions

FDD1 NCX x-coordinate of the normal line vector of the critical plane

FDD2 NCY y-coordinate of the normal line vector of the critical plane

FDD3 NCZ z-coordinate of the normal line vector of the critical plane

FDD1 NFX fracture plane component x

FDD2 NFY fracture plane component y

FDD3 NFZ fracture plane component z

FDD4 ALFA_DEV angle between critical and fracture planes

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